Since this distribution is implemented by adapting another distribution,
the tests consist of basic sanity checks computed by the R-2.5.1
Math library statistical package and its pbeta and dbeta functions.

In the following table v1 and v2
are the first and second degrees of freedom parameters of the distribution,
λ
is the non-centrality parameter, x is the random
variate, p is the probability, and q =
1-p.

Function

Implementation Notes

pdf

Implemented in terms of the non-central beta PDF using the relation:

f(x;v1,v2;λ) = (v1/v2) / ((1+y)*(1+y)) * g(y/(1+y);v1/2,v2/2;λ)

where g(x; a, b; λ) is the non central beta PDF, and:

y = x * v1 / v2

cdf

Using the relation:

p = By(v1/2, v2/2; λ)

where Bx(a, b; λ) is the noncentral beta distribution CDF and

y = x * v1 / v2

cdf complement

Using the relation:

q = 1 - By(v1/2, v2/2; λ)

where 1 - Bx(a, b; λ) is the complement of the noncentral beta
distribution CDF and